In the previous work, an efficient method has been proposed to represent solid objects as multiple combinations of globally
deformed supershapes. In this paper, this framework is applied with a new supershape implicit function that is based on the
notion of radial distance and results are presented on realistic models composed of hundreds of hierarchically globally deformed
supershapes. An implicit equation with guaranteed differential properties is obtained by simple combinations of the primitives’
implicit representations using R-function theory. The surface corresponding to the zero-set of the implicit equation is efficiently
and directly polygonized using the primitives’ parametric forms. Moreover, hierarchical global deformations are considered
to increase the range of shapes that can be modeled. The potential of the approach is illustrated by representing complex
models composed of several hundreds of primitives inspired from CAD models of mechanical parts.
Keywords implicit surface - solid modeling - superquadrics - supershape
A preliminary version of this paper appeared in Proc. Pacific Graphics 2005, Macau.
Yohan D. Fougerolle received his M.S. degree in electrical engineering from the University of Burgundy, Dijon, France, in 2002. He is a Ph.D.
candidate in electrical and computer engineering at the University of Burgundy, Le Creusot, France and was a visiting research
scholar in the Imaging, Robotics, and Intelligent Systems Laboratory, Knoxville, Tennessee from 2002 to 2005. His research
interests include computer vision, solid modeling and surface reconstruction.
Andrei Gribok is a research assistant professor in the Department of Computer and Electrical Engineering at the University of Tennessee,
Knoxville and also holds a position of an adjunct professor of statistics in the Department of Statistics at the same university.
His area of expertise is inverse and ill-posed problems in engineering, statistical learning and model misspecification in
statistics. His publications list includes three book chapters and numerous journal and conference papers. Dr. Gribok has
a B.S. degree in system science and an M.S. degree in nuclear engineering from the Moscow Institute of Physics and Engineering.
He received his Ph.D. degree from the Moscow Institute of Biological Physics in the area of acoustical pattern recognition,
artificial intelligence and nondestructive testing. He has 15 years of experience in industry as well as in academia. Dr.
Gribok worked as an invited scientist in the Cadarache Nuclear Research Centre in France where his work focused on nuclear
power plants monitoring, diagnostics and ultrasonic imaging.
Sebti Foufou received his Ph.D. degree in computer science in 1997 from the University of Claude Bernard Lyon I, France. He has been working
as an associate professor in the Computer Science Department at the University of Burgundy, France. His research interests
concern geometric modeling and CAD-CAM topics and surfaces blending, subdivision surfaces, and geometric constraints solving.
Currently, he is working as a temporary guest researcher at the National Institute of Standards and Technology, Gaithersburg,
Maryland, on smart machining systems, tolerances, assembly modeling, and PLM.
Frédéric Truchetet received his M.S. degree in physics from Dijon University, France, in 1973 and a Ph.D. degree in electronics from the same
university in 1977. He was for two years with Thomson-CSF as a research engineer and he is currently full professor in Le2i.
His research interests are focused on image processing for artificial vision inspection and particularly on wavelets transform,
multiresolution edge detection and image compression. He has authored and co-authored more than 150 international publications,
three books, and holds one patent. He is a member of GRETSI, ASTI, IEEE, SPIE, Chairman of SPIE’s conference on wavelet applications
in industrial processing and member of numerous technical committees of international conferences in the area of computer
vision.
Mongi A. Abidi is a professor and deputy director of the Department of Electrical and Computer Engineering, directs activities in the Imaging,
Robotics, and Intelligent Systems Laboratory. He received his Ph.D. degree in electrical engineering at The University of
Tennessee in 1987, M.S. degree in electrical engineering from the University of Tennessee in 1985, and principal engineer
in electrical engineering at the National Engineering School of Tunis, Tunisia in 1981. Dr. Abidi conducts research in the
field of 3D imaging, specifically in the areas of scene building, scene description, and data visualization.